In a large skillet, melt butter and olive oil on medium high heat.
Dredge chicken in seasoned flour and fry in butter/olive oil mixture until golden brown, about 5 minutes on each side. Remove from pan and set aside.
Using the same pan, add mushrooms and garlic; sauté for a few minutes until mushrooms are tender and lightly browned.
Add white wine and thyme and bring to a boil. Add chicken back to pan and simmer for about 15-20 minutes. Remove chicken from pan. Add cream, asiago, and Dijon to the pan; stir to combine. Season with salt and pepper to taste. Add chicken back to pan and simmer until heated through.